A JWST Transiting Survey of FGK Stellar Limb Darkening: Empirical Evidence for Quadratic Laws and Atmospheric Model Comparisons

Abstract

We present a study of stellar limb darkening using JWST transit observations of seven exoplanets orbiting FGK host stars, spanning 4200–6800 K. The wide wavelength coverage and high S/N of NIRISS/SOSS and NIRSpec/PRISM enable precise constraints on the wavelength-dependent limb darkening. Using Bayesian model selection, we find that the quadratic limb-darkening law is statistically preferred over higher-order laws for most FGK stars, recovers consistent intensity profiles for >95% of the stellar disk area, and introduces a minimal bias in the derived transit depths of only ∼14 ppm (1σ) for 6/7 targets. This contrasts with previous studies relying on stellar models. We compare the empirically derived quadratic coefficients to predictions from the PHOENIX, MPS-ATLAS, MURaM, and Stagger stellar atmosphere grids. We introduce a quadratic limb-darkening parameterization in terms of limb intensity (ℓ) and curvature at mid-μ (δ), finding that empirical FGK limb darkening is generally more linear than models predict (δ ≲ 0.1). We identify wavelength-independent offsets between data and model quadratic coefficients, minimized by adopting μmin=0.2 in intensity calculations; we attribute this in part to models overpredicting limb darkening near the limb where the plane-parallel approximation breaks down. For spherical PHOENIX models, we derive a μ rescaling method using a τ = 1 photospheric radius. With these corrections, residual offsets are minimized and all stellar models achieve statistically acceptable fits. We provide recommended limb-darkening offset priors for use in JWST transit analyses, enabling more accurate constraints on exoplanet transmission spectra while accounting for residual stellar model uncertainties.